We use the finite Markov chain embedding technique to obtain the distribution of the number of cycles in the breakpoint graph of a random uniform signed permutation. This further gives a very good approximation of the distribution of the reversal distance between two random genomes.

Simona Grusea, "On the Distribution of the Number of Cycles in the Breakpoint Graph of a Random Signed Permutation", IEEE/ACM Transactions on Computational Biology and Bioinformatics, vol. 8, no. , pp. 1411-1416, September/October 2011, doi:10.1109/TCBB.2010.123